Specific heat of the $S=1$ spin-dimer antiferromagnet ${\mathrm{Ba}}_3{\mathrm{Mn}}_2{\mathrm{O}}_8$ in high magnetic fields

We have measured the specific heat of the coupled spin-dimer antiferromagnet ${\mathrm{Ba}}_3{\mathrm{Mn}}_2{\mathrm{O}}_8$ to $50\mathrm{mK}$ in temperature and to $29\mathrm{T}$ in the magnetic field. The experiment extends to the midpoint of the field region $(25.9\mathrm{T}⩽H⩽32.3\mathrm{T})$ of the magnetization plateau at $1∕2$ of the saturation magnetization, and reveals the presence of three ordered phases in the field region between that of the magnetization plateau and the low-field spin-liquid region. The exponent of the phase boundary with the thermally disordered region is smaller than the theoretical value based on the Bose-Einstein condensation of spin triplets. At zero field and $29\mathrm{T}$, the specific-heat data show gapped behaviors characteristic of spin liquids. The zero-field data indicate that the gapped triplet excitations form two levels whose energies differ by nearly a factor of 2. At least the lower level is well localized. The data at $29\mathrm{T}$ reveal that the low-lying excitations at the magnetization plateau are weakly delocalized.

Figure 1

Temperature dependence of the specific heat of ${\mathrm{Ba}}_3{\mathrm{Mn}}_2{\mathrm{O}}_8$ in constant magnetic fields between $9\mathrm{T}$ and $18\mathrm{T}$. The nuclear contribution of ${}^{55}\mathrm{Mn}$ is visible at temperatures below $0.2\mathrm{K}$.

Figure 2

Specific heat of ${\mathrm{Ba}}_3{\mathrm{Mn}}_2{\mathrm{O}}_8$ in constant magnetic fields ranging from $19.5\mathrm{T}$ to $26\mathrm{T}$. The lines are guides to the eye.

Figure 3

Magnetic-field dependence of the specific heat of ${\mathrm{Ba}}_3{\mathrm{Mn}}_2{\mathrm{O}}_8$. The transition points are indicated by arrows. The lines are guides to the eye.

Figure 4

Magnetic phase diagram of ${\mathrm{Ba}}_3{\mathrm{Mn}}_2{\mathrm{O}}_8$. The circles are the positions of the peaks and shoulders in the specific heat at constant magnetic fields. The diamonds are the positions of the peaks and shoulders in the specific heat measured as a function of the magnetic field, while the current for the reservoir heater was held constant. The lines are guides to the eye.

Figure 5

Temperature dependence of the specific heat of ${\mathrm{Ba}}_3{\mathrm{Mn}}_2{\mathrm{O}}_8$ at $0\mathrm{T}$ and $29\mathrm{T}$. The thick solid lines are the low-temperature fits to the data. The dashed line indicates the calculated zero-field specific heat due to localized, gapped excitations, whose parameters are taken from the low-temperature fit. The thin solid line is the specific heat due to two kinds of localized excitations with two gap energies, as described in the text. The dotted line for the $29\mathrm{T}$ data indicates the specific heat of mutually isolated dimers with an excitation gap of $\Delta =4.3\mathrm{K}$. In the inset, $\ln \left(C{T}^2\right)$ of the zero-field data have been plotted against $1∕T$ to reveal the localized-excitation behavior, which is given by the straight line. The deviation of the data from the line at temperatures below $1.4\mathrm{K}$ is due to the phonon contribution and an uncertainty in the subtraction of the background heat capacity of the silver paint.